Optimal versus robust inference in nearly integrated non-Gaussian models

Elliott, Rothenberg, and Stock (1996, Econometrica 64, 813-836) derive a class of point-optimal unit root tests in a time series model with Gaussian errors. Other authors have proposed "robust" tests that are not optimal for any model but perform well when the error distribution has thick tails. I derive a class of point-optimal tests for models with non-Gaussian errors. When the true error distribution is known and has thick tails, the point-optimal tests are generally more powerful than the tests of Elliott et al. (1996) and also than the robust tests. However, when the true error distribution is unknown and asymmetric, the point-optimal tests can behave very badly. Thus there is a trade-off between robustness to unknown error distributions and optimality with respect to the trend coefficients.